Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games

Werner Krabs

ISBN 10: 3540403272 / ISBN 13: 9783540403272

Published by Springer Berlin Heidelberg Aug 2003, 2003

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -Focuseson the analysis, optimization and controllability of time-discrete dynamical systems and games under the aspect of stability, controllability and (for games) cooperative and non-cooperative treatment. The investigation of stability is based on Lyapunov's method which is generalized to non-autonomous systems. Optimization and controllability of dynamical systems is treated, among others, with the aid of mapping theorems such as implicit function theorem and inverse mapping theorem. Dynamical games are treated as cooperative and non-cooperative games and are used in order to deal with the problem of carbon dioxide reduction under economic aspects. The theoretical results are demonstrated by various applications. 204 pp. Englisch.

Seller Inventory # 9783540403272

Bibliographic Details

• Title: Analysis, Controllability and Optimization of Time-Discrete Systems and Dynamical Games
• Publisher: Springer Berlin Heidelberg Aug 2003
• Publication Date: 2003
• Language: English
• ISBN 10: 3540403272
• ISBN 13: 9783540403272
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 12D millimeters 235 millimeters width by 155 millimeters height by 12 millimeters depth
• Weight: 318 grams

About this title

Synopsis

J. P. La Salle has developed in [20] a stability theory for systems of difference equations (see also [8]) which we introduce in the first chapter within the framework of metric spaces. The stability theory for such systems can also be found in [13] in a slightly modified form. We start with autonomous systems in the first section of chapter 1. After theoretical preparations we examine the localization of limit sets with the aid of Lyapunov Functions. Applying these Lyapunov Functions we can develop a stability theory for autonomous systems. If we linearize a non-linear system at a fixed point we are able to develop a stability theory for fixed points which makes use of the Frechet derivative at the fixed point. The next subsection deals with general linear systems for which we intro­ duce a new concept of stability and asymptotic stability that we adopt from [18]. Applications to various fields illustrate these results. We start with the classical predator-prey-model as being developed and investigated by Volterra which is based on a 2 x 2-system of first order differential equations for the densities of the prey and predator population, respectively. This model has also been investigated in [13] with respect to stability of its equilibrium via a Lyapunov function. Here we consider the discrete version of the model.